Hello Pravakar,
If you want to migrate an entire server that includes a website to Google Cloud Platform, then this step-by-step guide can help. Once you are done with the migration, you would have to adjust the website settings to make use of the new network and infrastructure. For example, you may need to change your Domain name settings, and modify some links to reflect on the new IP address of the VM instance. Here are further documents about Cloud DNS, static IPs, and general options hosting websites on Google Cloud Platform.
Pravakar,
Since you may not have access to the server, I think the easiest solution in this case is to build a new Prestashop VM using cloud Launcher on Google Cloud Platform like this example. Once deployed, you will have instructions on how to access the server and its database. Then, you would need to find a way to backup your existing website’s data ( files and DB) from your host (probably through cpanel if it is offered), and move them over to that VM instance. I found these articles [1] [2] that could be useful for your use case. For more information about the example above you may check this bitnami document.
Another option, if you have access to the website’s home directory, could be building a raw VM instance, and copy everything over including the database (if on the same server) using your tool of choice.
As this question seems more related to migrating from your hosting provider, I suggest checking with them on the options and tools available to transfer your current setup. Furthermore, and for further help you may post your question at PrestaShop’s forum as they are more equipped to help with exporting your data.